7.5.2 The Galaxian Age-Metallicity Relation

In Figure we plot
,
,
and
versus
.
Both
and
are highly (anti-)correlated with
.
Part of the age-metallicity relation
may be due to measurement errors.
This is because the lines of constant age and metallicity are not
quite perpendicular to each other in the
-
and
-
diagrams
(see Fig. ).
To quantify this effect,
Monte-Carlo simulations are needed.
This is planned for a future extension of this work.

is not significantly correlated with
.
For the combined HydraI+Coma sample,
we find
%.

A fit to the Mg and Fe age-metallicity relations
for the combined HydraI+Coma sample
gives

(7.27)

and

(7.28)

The `mixed' relation with
and
,
which is what is plotted in Fig. (c-d), gives

(7.29)

We also tried to include a
term
in the age-metallicity relations.
Still for the combined HydraI+Coma sample, a fit gives

(7.30)

and

(7.31)

The
terms are highly significant.
The two relations look similar,
but there is the important difference,
that while
is correlated with
(
%),
is not significantly correlated with
(
%).
Both
and
are correlated with
(
% and
%, respectively).
There is also the difference, that for the Mg relation the scatter
decreases when we add a
term,
while it increases for the Fe relation.
We also fitted the `mixed' relation with
and
.
The result is
,
with
.
As can be seen from the bootstrap uncertainties,
the relation is not well defined.

The above restates the result from
Worthey, Trager, & Faber (1995),
that
(a) there is an age-metallicity relation
with a large span in age, and
(b) galaxies of higher velocity dispersion follow an age-metallicity relation
at higher metallicity (or older age).
These authors used
the index C24668 and several Balmer line indices
(probably
,
,
and
)
to derive mean metallicities and ages,
not
and
(or
and
)
as we did.
It is therefore encouraging that our result is in qualitative agreement
with their result.

Worthey et al. report that they
were not able to establish the slope nor the zero point of this
age-metallicity-sigma relation.
No doubt they could have made a fit to their data,
so what they mean is probably that the different indices give different
ages and metallicities. For example, they find
that an Mg index gives a significantly different age than
an Fe index.
While we also find our two ages to be significantly different,
the size of this difference is small.
In accordance with this,
the coefficients for `
' in Eq. () and
() are not significantly different.
We are not able to establish the true zero point.

We can now revisit two problems raised earlier,
namely the interpretation of
(a) the intrinsic scatter in the
-
relation, and
(b) the similar intrinsic scatter in the FP in
Gunn r, Johnson B, and Johnson U.

If we take the Mg-version of the age-metallicity-sigma relation
(Eq. )
at face value
and insert it
in the analytical approximation to the predictions from the
Vazdekis et al. models for
(J97; Eq. ),
we can eliminate either
or
.
We get

(7.32)

where the constants c and d depend on
.
This means that due to the relation between age and metallicity
for a given sigma the
index changes very little as either age or
metallicity changes.
Using these relations,
the intrinsic scatter in the
-
relation of 0.024
translates into a
variation of 0.8 dex
or a
variation of 0.6 dex,
both at a given
.
This is much larger than the estimates obtained without the
age-metallicity-sigma relation taken into account,
0.2 dex and 0.13 dex.
Worthey et al. (1995) also reached the conclusion that
when taking into account the age-metallicity relation,
the intrinsic scatter in the
-
relation
allowed for a larger variation in age than 15%.
If we had excluded the 5 (out of 155) galaxies that have very large residuals
from the
-
relation,
the intrinsic scatter would be 0.014,
which translates into either 0.45 dex in
or 0.35 dex in
.
The corresponding numbers without taking into account the
age-metallicity-sigma relation are
0.13 dex and 0.08 dex, respectively.

In a similar manner, we insert the Mg-version of the
age-metallicity-sigma relation (Eq. )
into the analytical approximations to the predictions from the
Vazdekis et al. models for
(Eq. -).
When eliminating either
or
,
the result is

(7.33)

where the constants ci and di depend on
.
It is seen that the coefficients for
and
vary much less with passband than
when the age-metallicity-sigma relation is not taken into account,
see Eq. ()-(),
p. .
Therefore, if we explain the intrinsic scatter in the FP
(interpreted as the
relation)
by either an age variation at a given sigma and metallicity,
or a metallicity variation at a given sigma and age,
the scatter in
is not expected to be very different in the
different passbands, in agreement with the observations.

The intrinsic scatter in the
relation is 0.103 dex in
Gunn r.
This translates into a variation in
of 0.24 dex,
or a variation in
of 0.19 dex.
This is substantially less than the variation needed to explain the intrinsic
scatter in the
-
relation in the same way.
Since we do not have a detailed understanding of the origin of these two
relations, it might well be, that galaxy formation and evolution
made
be less well determined from
than
from mass.